· Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z be its length. Show that (a) V(2²) = 2r. (b) V(1/2) = -îjr². (c) What is the general formula for V(2ª)?

Q: Find the maximum rate of change of f(x, y) = ln(x² + y2) at the point (-3, -5) and the direction in…

A:

Q: Let L be the line passing through the point P(1, 1, 1) with direction vector d=[2, 1, 0]T. Find the…

A:

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

A:

Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

A:

Q: The vector n = (2, -3, 6) is normal to the tangent plane to z = h(x, y)at (1, -3, 5). Estimate…

A:

Q: Q3. For the motion vector r(t) = e'cost i + e'sint j , find: (i) (ii) ат

A:

Q: Q4\A: Find area of zone bounded by curves x = y? 2y = x-3 B: Find area of triangle whose vectors…

A:

Q: Consider the following function and point F f(x, y) = /E (a) Find the unit vectors in the direction…

A:

Q: Let h(x, y) = x² + 3xy - 6y. In what direction does h increase most rapidly at the point (3, 2)? (a)…

A:

Q: 22. Given the symmetric equations t = - and t = +', find the vector equation of the line.

A:

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: br II) passing through P=(2,-1) and is perpendiculed to the line √x=2-t y=3 In normal form.

A:

Q: Given u(t) = (e',e-t). a) Find: (i) u'(t) (ii) u"(t) b) Find the unit tangent

A:

Q: If (a,B), a<o is the unit vector that is parallel to the tangent line to the curve y=3x2-x at the…

A:

Q: Q5/A// Find the distance between the point P =(2, 1, 1) and line L:x = -2+ 5t, y= 2 +4t, z = -3-6t.…

A: Use distance formula